Question

Determine whether each statement is true or false. if true, explain your reasoning . If false provide a counter example.

Answer 1

Answer:

1. False

2. False

3. True

Step-by-step explanation:

1. The diagonals of a rectangle always form four congruent triangles, which is a false statement.

The counter-statement will be, the diagonals of a square always form four congruent triangles.

2. A quadrilateral has perpendicular diagonals. Is this enough to determine what type of quadrilateral it is?

The answer is no.

The counter-statement will be, a quadrilateral has perpendicular diagonals, then it may be a rhombus or a square.

3. Explain why drawing a diagonal on any parallelogram will always result in two congruent triangles and it is true that the two triangles will be congruent as the opposite sides of the parallelogram are equal and there is a common side which is the diagonal itself.

Therefore, using SSS criteria the triangles are congruent. (Answer)